Enumerative Real Algebraic Geometry

Let C be a smooth real plane curve. Let c be its degree and g its genus. We assume that C has at least g real branches. Let d be a nonzero natural integer strictly less than c. Let e be a partition of cd of length g. Let n be the number of all real plane curves of degree d that are tangent to g real branches of C with orders of tangency e1; . . . ; eg. We show that n is finite and we determine n explicitly. Key words. Enumerative geometry, real algebraic curve, real branch, M-curve,

• Type: Conference
• Year: 2001
• Where: DIMACS
• Authors: Frank Sottile
• Keywords: DIMACS 2001, Real Branches, Real Plane Curve, Smooth Real Plane, Theoretical Computer Science